the sum of two positive intergers a ,and b , is atleast 30 the difference of the two intergers is atleast 10 . if b is the greater interger which system of inqualites could represent the vaules of a and b

James is playing his favorite game at the arcade. after playing the game 3 times, he has 8 tokens remaining. he initially had 20 tokens, and the game costs the same number of tokens each time. the number tt of tokens james has is a function of gg, the number of games he plays

Solve the equation - 2(m -30) = -6m a-15 b-13 c-8 d8

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?